Satellite communication is widely used to provide communication in a variety of military, commercial, and consumer applications. These communications take place between a satellite and a ground station and/or receivers at various positions on Earth.
Global Positioning Satellite (GPS) systems have been widely used since the 1980's to provide positioning information to a receiver for commercial utilization within the United States. Such global positioning systems are used elsewhere in the world and, for example, Russia operates a similar system (GLONASS) and the European Union is developing a third system “Galileo”.
GPS systems use a combination of orbiting satellites and land stations to communicate with a receiver to provide signals which may be utilized to determine the position of the receiver. Such global positioning systems are widely used for a variety of commercial purposes including providing vehicular travel location assistance, common surveying systems, a variety of agricultural and commercial applications, and/or military usage.
GPS receivers normally determine their position by computing relative times of arrival of signals transmitted simultaneously from a multiplicity of GPS satellites. By determining the relative time of arrival from each satellite, a pseudorange to that satellite can be calculated (e.g., by multiplying speed of light by the relative time). Position of a receiver on Earth can then be calculated once pseudoranges to the satellites are known.
Therefore, Global Navigation Satellite Systems (GNSS) navigation requires two steps. First, a GPS signal must be acquired and tracked by a receiver in order to calculate the pseudorange to each satellite. Secondly, the receiver needs to have accurate knowledge of the satellite positions in order to geometrically calculate the position of the receiver. The second problem is solved by providing an orbit model for the GPS constellation which is fit to the true satellite positions using a series of constant coefficients which are transmitted as part of the GPS data message. Both of these tasks become more difficult in a weak signal environment. Substantial research has been completed on the first problem suggesting the capability of acquiring and tracking GPS signals as low as 15 dB-Hz. In order to accurately download the GPS broadcast ephemeris, a high signal strength is necessary for a minimum predetermined period. This makes the second problem significantly more challenging in a weak signal environment as the orbit data will not be available as often. Significant progress has been made in formulating a GPS ephemeris capable of longer accurate propagation allowing a greater latency between the availability of new orbit data.
Once a receiver on Earth is powered, it locates and locks on to the satellites to which it has lines of sight. Thereafter, the receiver requires reception of satellite positioning data, as well as data on clock timing (ephemeris data). The ephemeris data is provided to the receiver by communicating coefficients associated with orbital parameters listed in table 1, below. The communication of the orbital parameters from the satellites is referred to as the broadcast ephemeris.
TABLE 1Broadcast Ephemeris DataParameterDescriptionMoMean Anomaly at Reference TimeΔnMean Motion Difference From KeplerianeEccentricity{square root over (A)}Square Root of the Semi-Major AxisΩoLongitude of Ascending Node of Orbit Plane atWeekly EpochioInclination Angle at Reference TimeωArgument of PrelapsisΩRight Ascenscion Linear Rate of ChangeIDOTInclination Linear Rate of ChangeCUCAmplitude of Harmonic Cosine Correction to Argumentof LattitudeCUSAmplitude of Harmonic Sine Correction to Argumentof LattitudeCRCAmplitude of Harmonic Cosine Correction to Orbit RadiusCRSAmplitude of Harmonic Sine Correction to Orbit RadiusCICAmplitude of Harmonic Cosine Correction to InclinationCISAmplitude of Harmonic Sine Correction to InclinationTOEReference Time of EphemerisIODEIssue of Data
The broadcast ephemeris (BE) data is currently used by GPS receivers to calculate the satellites' current positions and the satellites' future positions up to a particular time into the future. An algorithm for determining the satellites' positions using the orbital parameters listed in Table 1 is provided in Navstar global positioning system interface specification (is-gps-200d) which can be found at http://www.navcen.uscg.gov/pdf/IS-GPS-200D.pdf (2004).
Determining satellites' positions based on the BE data, however, poses three challenges. First, in order to determine the satellites positions from the BE data, the BE data must be received at a sufficiently low bit error rate (BER). In order to maintain a sufficiently low BER it has been found the GPS signal must be tracked with a signal to noise ratio of at least 27 dB-Hz (see Spilker Jr. J. J. and Parkinson B. W. Global Positioning System: Theory and Applications, Vol. 1. American Institute of Aeronautics and Astronautics Inc, 1996). Second, the BE data provides an orbit model which is valid for a short period of time (e.g., four to six hours). Therefore if a receiver is operating in a weak signal environment, where the signal to noise ratio is below 27 dB-Hz, the receiver becomes unable to determine the satellite's positions. Third, because the receiver require fresh BE data downloaded from the satellites at least at expiration of validity periods of the BE data, in cases where the receiver is a handheld unit, the repeated downloads can drain the receiver's battery. This is especially problematic since reception of the complete BE data takes about 30 seconds.
In some applications, for example global asset tracking, it is not desirable to require continuous transmission of ephemeris data to all receivers in the field. Receivers could be deployed in the field for long periods of time, switching on only once per day, for a few seconds, to collect GPS signals, compute, and transmit their positions. Limiting the data collection interval to the minimum required to achieve a detectable signal to noise ratio would greatly increase the battery life.
To address the second and third issues discussed above (i.e., short period of validity as well as excessive battery usage) an extended propagation ephemeris (EPE) model was developed and described in U.S. Pat. No. 7,679,550 to Garrison et al. (hereinafter the ‘550 patent), incorporated herein by reference in its entirety, that can estimate positions of satellites for extended times (24 hours to 72 hours) well beyond the period of validity of the BE data. The EPE model uses a high accuracy satellite positional model or historical data of actual positional data of the satellites to determine coefficients that define the model. A least square algorithm was used to determine coefficients that define osculating orbital elements (i.e., semi-major axis (a), eccentricity (e), inclination (i), right ascension of the ascending node (Ω), argument of perigee (ω), and true anomaly (θ*)) and harmonic perturbation parameters in a coordinate system (e.g., the radial coordinate system (RSW)). The original EPE model used the least square filter to minimize the positional errors (i.e., estimated positions vs. actual positions) by modifying coefficients β1 through β23, and coefficients α1 through α10. Dominant frequencies for fθ*, fR1, fR2, fS1, fS2, and fW1 are obtained through Fourier transforms. The coefficients (i.e., β1 through β23, and coefficients α1 through α10) and the dominant frequencies (i.e., fθ*, fR1, fR2, fS1, fS2, and fW1) are then loaded on to the receiver to estimate position of the satellites using the following set of equations.â=β1+β2θ+β3 cos(2πfaθ)+β4 sin(2πfaθ)ê=β5+β6θ+β7 cos(2πfe1θ)+β8 sin(2πfe1θ)+β9 cos(2πfe2θ)+β10 sin(2πfe2θ)î=β11+β12θ+β13 cos(2πfiθ)+β14 sin(2πfiθ){circumflex over (Ω)}=β15+β16θ+β17 cos(2πfΩ1θ)+β18 sin(2πfΩ1θ){circumflex over (θ)}*=β19+β20t+β21 cos(2πfθ*1t)+β22 sin(2πfθ*1t){circumflex over (ω)}=β23 δR=α1 cos(2πfR1t)+α2 sin(2πfR1t)+α3 cos(2πfR2t)+α4 sin(2πR2t)δS=α5 cos(2πfS1t)+α6 sin(2πfS1t)+α7 cos(2πfS2t)+α8 sin(2πS2t)δW=α9 cos(2πfW1t)+α10 sin(2πfW1t)  (B1)These coefficients and dominant frequencies are communicated to the receiver by a ground station and are used by the receiver to estimate positions of the satellites.
As indicated above, in the original EPE model it was assumed that the fθ* term for the true anomaly (θ*) is determined by applying a Fourier Transform (e.g., discrete Fourier transform (DFT)) to the calculated orbital elements. The frequency resolution of DFT is defined by:Δf=fs/n  (B2)where, fs is the sampling frequency, andn is the number of samples which is defined by:n=TdatafS  (B3)where Tdata is the data length. The term fθ* determined by applying the Fourier transform results in extreme susceptibility to directional root mean square (RMS) errors for the model. Therefore, there is a need to determine the term fθ* besides finding the Fourier transform.
In addition, the original EPE model has a limitation that is shared with the GPS BE data which is the error between the estimated orbital positions of the satellites and the actual positions will be relatively uniform within the fit interval (24 or 72 hours), but will increase greatly outside of it. Therefore, it is also desirable to define a new EPE model that, for the same amount of data, would have a higher accuracy at the start of the least square fit, and has a gradual reduction in accuracy as the time from beginning of the validity of the EPE model (i.e., 24 to 72 hours) increases.